Judgelight: Trajectory-Level Post-Optimization for Multi-Agent Path Finding via Closed-Subwalk Collapsing

TL;DR

Judgelight introduces MAPF-Collapse, a trajectory-level post-processing framework that collapses closed subwalks in a given feasible MAPF schedule to minimize move actions while preserving all feasibility constraints. The authors prove MAPF-Collapse is NP-hard and provide an exact ILP formulation that encodes candidate collapses, their savings, and inter-agent dependencies, along with practical preprocessing to prune the action space. Empirical results on the POGEMA benchmark show that Judgelight consistently reduces solution cost by roughly 20%–40%, with most instances solved within one second, and yields particular gains for learning-based MAPF solvers. This post-optimization step is solver-agnostic and readily applicable to MAPF variants, offering a practical path to deploy more efficient multi-robot plans in real-world settings.

Abstract

Multi-Agent Path Finding (MAPF) is an NP-hard problem with applications in warehouse automation and multi-robot coordination. Learning-based MAPF solvers offer fast and scalable planning but often produce feasible trajectories that contain unnecessary or oscillatory movements. We propose Judgelight, a post-optimization layer that improves trajectory quality after a MAPF solver generates a feasible schedule. Judgelight collapses closed subwalks in agents' trajectories to remove redundant movements while preserving all feasibility constraints. We formalize this process as MAPF-Collapse, prove that it is NP-hard, and present an exact optimization approach by formulating it as integer linear programming (ILP) problem. Experimental results show Judgelight consistently reduces solution cost by around 20%, particularly for learning-based solvers, producing trajectories that are better suited for real-world deployment.

Figures (6)

• Figure 1: We create three agents $A_1$, $A_2$, and $B_{e_1}$. The given paths are $A_1$: {$x_1$, $p_1$, $p_1$, $p_1$, $p_1$, $p_1$, $x_1$}, $A_2$: {$x_2$, $p_2$, $p_2$, $p_2$, $p_2$, $p_2$, $x_2$}, and $B_{e_1}$: {$a_{e_1}$, $x_1$, $b_{e_1}$, $c_{e_1}$, $a_{e_1}$, $x_2$, $b_{e_1}$}. In this example, the optimal collapsed schedule collapses either $\{A_1, B_{e_1}\}$ or $\{A_2, B_{e_1}\}$.
• Figure 2: We create six agents $A_1$, $A_2$, $A_3$, $B_{e_1}$, $B_{e_2}$, and $B_{e_3}$. The given paths are $A_1$: {$x_1$, $p_1$, …, $p_1$, $x_1$}, $A_2$: {$x_2$, $p_2$, …, $p_2$, $x_2$}, $A_3$: {$x_3$, $p_3$, …, $p_3$, $x_3$}, $B_{e_1}$: {$a_{e_1}$, $x_1$, $b_{e_1}$, $c_{e_1}$, $a_{e_1}$, $x_2$, $b_{e_1}$, …, $b_{e_1}$}, $B_{e_2}$: {$a_{e_2}$, …, $a_{e_2}$, $x_2$, $b_{e_2}$, $c_{e_2}$, $a_{e_2}$, $x_3$, $b_{e_2}$, …, $b_{e_2}$}, and $B_{e_3}$: {$a_{e_3}$, …, $a_{e_3}$, $x_1$, $b_{e_3}$, $c_{e_3}$, $a_{e_3}$, $x_3$, $b_{e_3}$}. All agents' paths have length 21. In this example, we can collapse at most one vertex-agent $A_i$. However, regardless of which $A_i$ is collapsed, each edge-agent $B_{e_r}$ can always be collapsed once. The only difference is that the choice of $A_i$ determines which collapse option is feasible for the incident edge-agents.
• Figure 3: Examples of POGEMA-tested maps. Maze and Random map sizes are 32x32. Warehouse map is 33x46. Puzzle map sizes are below 10x10. Cities-tiles are 64×64 areas selected from larger Cities maps.
• Figure 4: This figure illustrates how Judgelight performance is affected by testcase difficulty and algorithm performance. We include only test cases for which the algorithm achieves $\mathrm{ISR}=1$, as Judgelight's cost savings are not meaningful when agents exhibit largely random motion (even though the apparent savings could be high in such cases). Missing data indicate that the algorithm has no suitable test cases under the corresponding experimental settings.
• Figure 5: In this figure, we include only test cases for which the algorithm achieves $\mathrm{ISR}>0.5$. This choice was made to provide more informative test cases. An $\mathrm{ISR}>0.5$ indicates that the learning-based policy is still partially effective on the test case. While such performance may not be sufficient for the MAPF task, it may still be useful for LMAPF.

Theorems & Definitions (4)

• lemma thmcounterlemma
• proof
• theorem thmcountertheorem
• proof